The guide
Everything here is the chain rule plus enough engineering to make it train. That is not a dismissal. The engineering is where almost all the difficulty lives.
Notice how much of this topic is stability rather than capability. Softmax subtracts a maximum so exponentials do not overflow. Cross entropy is fused with softmax so the gradient stays simple. Normalisation layers keep activations in a range where gradients survive many layers. Gradient clipping stops one bad batch destroying the run. Adam adapts a learning rate per parameter because one global rate never suits everything.
Attention is the exception and the reason the last decade looks the way it does. It lets every position look at every other directly, rather than passing information along a chain and hoping it survives.